Tidally induced stellar oscillations: converting modelled oscillations excited by hot Jupiters into observables

TL;DR

This paper models how hot Jupiters induce stellar oscillations and predicts observable spectroscopic and photometric signals, highlighting differences from equilibrium tide models and discussing detection prospects.

Contribution

It introduces a detailed conversion from tidally induced stellar oscillations to observable signals, considering non-adiabatic effects and convective flux perturbations.

Findings

Photometric signal scales as P^{-2}

Radial velocity signal scales as P^{-1}

Radial velocity signals are stronger at longer periods

Abstract

We calculate the conversion from non-adiabatic, non-radial oscillations tidally induced by a hot Jupiter on a star to observable spectroscopic and photometric signals. Models with both frozen convection and an approximation for a perturbation to the convective flux are discussed. Observables are calculated for some real planetary systems to give specific predictions. Time-dependent line broadening and the radial velocity signal during transit are both investigated as methods to provide further insight into the nature of the stellar oscillations. The photometric signal is predicted to be proportional to the inverse square of the orbital period, $P^{-2}$, as in the equilibrium tide approximation. However, the radial velocity signal is predicted to be proportional to $ P^{-1}$, and is therefore much larger at long orbital periods than the signal corresponding to the equilibrium tide approximation, which is proportional to $P^{-3}$. The prospects for detecting these oscillations and the implications for the detection and characterisation of planets are discussed.